{"id":51010,"date":"2025-01-17T11:56:41","date_gmt":"2025-01-17T16:56:41","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&p=51010"},"modified":"2025-06-24T10:16:03","modified_gmt":"2025-06-24T14:16:03","slug":"ams-weekly-seminar-karthik-shekhar","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-karthik-shekhar\/","title":{"rendered":"AMS Weekly Seminar | Karthik Shekhar"},"content":{"rendered":"

Location:\u00a0<\/strong>Gilman 50<\/p>\n

When:<\/strong> May 1st at 1:30 p.m.<\/p>\n

Title:\u00a0<\/strong>S<\/span>patiotemporal Ionic Dynamics at the Interfaces of Biological Membranes<\/span><\/p>\n

Abstract:<\/span><\/strong> <\/span>Electrical activity in biological systems arises from transmembrane ionic currents passing through sub-nanometer pores in ion channels and pumps. Although<\/span> acting as<\/span> localized<\/span>\u201csources\u201d and \u201csinks\u201d<\/span> on the cell<\/span>ular lipid<\/span> membrane<\/span>s<\/span>, these discrete currents trigger large-scale events such as neurotransmission and muscle contraction.<\/span> T<\/span>he dominant approach for studying electrical signaling in biology relies on \u201cequivalent circuit\u201d models<\/span> (e.g., Hodgkin and Huxley, 1952)<\/span>, which coarse-grain the microscopic <\/span>and localized nature <\/span>of ion channel currents. While these models <\/span>phenomenologically<\/span> capture many macroscopic observations, they leave the direct mechanistic link between microscopic ionic currents and <\/span>the ensuing<\/span> spatiotemporal <\/span>phenomena<\/span><\/span>largely opaque<\/span>.<\/span><\/p>\n

In this talk, I will argue that bridging this gap requires a precise understanding of <\/span>how these localized sources and sinks drive electrochemical reorganization at the <\/span>cellular <\/span>membrane interface<\/span>.<\/span>\u00a0<\/span>I will present a mathematical framework based on the Poisson\u2013Nernst\u2013Planck (PNP) equations, a <\/span>nonlinear <\/span>system of coupled PDEs. Using large-scale finite element simulations and analytical theory, <\/span>I will show how nontrivial dynamical scaling behaviors emerge in the spatiotemporal evolution of charge during localized transmembrane currents<\/span> (<\/span>arXiv:2407.11947<\/span>)<\/span>.<\/span><\/span>I will then discuss ongoing efforts to extend this framework to spherical vesicles and cylindrical tubular membranes, highlighting how membrane geometry influences electrochemical reorganization.\u00a0Finally, I will demonstrate that<\/span> in all cases,<\/span> <\/span>a boundary layer theory yields analytical expressions that fully explain the numerical <\/span>results and<\/span> highlight the role of long-ranged electrostatic effects in ionic reorganization<\/span>. These findings allow us to visualize <\/span>the resulting dynamical regimes<\/span> in<\/span> <\/span>space\u2013time diagrams and to derive analytical expressions that can be applied to<\/span> study emergent behavior in<\/span> <\/span>stochastic simulations<\/span> of electrostatically coupled ion channels and pumps<\/span>.<\/span><\/span><\/p>\n

Bio:<\/span> <\/span><\/strong>Karthik\u00a0Shekhar\u00a0is the John F. Heil Jr Assistant Professor in the Department of Chemical and<\/span> <\/span>Biomolecular Engineering at the UC Berkeley. His undergraduate (IIT Bombay) and graduate<\/span> <\/span>(MIT) degrees are in chemical engineering<\/span>, while<\/span> <\/span>h<\/span>is research as a postdoc was at the intersection<\/span> <\/span>of single-cell genomics and neuroscience (Broad Institute). His research group at UC Berkeley<\/span> <\/span>focuses on problems in neuroscience and biophysics through a synthesis of theoretical,<\/span><\/span>computational, and data-driven approaches. He has received fellowships from the McKnight<\/span><\/span>Foundation, Hellman Foundation, and the Glaucoma Research Foundation. He <\/span>is a recipient of the<\/span> Donald E. Noyce Prize for university-wide<\/span> <\/span>excellence in undergraduate teaching.<\/span><\/p>\n

Zoom link:<\/strong> https:\/\/wse.zoom.us\/j\/93287142219?pwd=z9fqWnRMzmzS0SGijRiie5yN3kHRSZ.1<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Location:\u00a0Gilman 50 When: May 1st at 1:30 p.m. Title:\u00a0Spatiotemporal Ionic Dynamics at the Interfaces of Biological Membranes Abstract: Electrical activity in biological systems arises from transmembrane ionic currents passing 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